Appendix A Answers to End-of-Chapter Practice …978-3-319-00630-7/1.pdfAppendix A Answers to End-of-Chapter Practice Problems Chapter 1: Practice Problem #1 Answer (see Fig. A.1)
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Appendix A
Answers to End-of-Chapter Practice
Problems
Chapter 1: Practice Problem #1 Answer (see Fig. A.1)
(a) Create an Excel table for these data, and then use Excel to the right of the table
to find the sample size, mean, standard deviation, and standard error of the mean
for these data. Label your answers, and round off the mean, standard deviation,
and standard error of the mean to two decimal places.
(b) Save the file as: CONCRETE3
Chapter 2: Practice Test
Suppose that an engineer who works for an automobile manufacturer wants to take
a random sample of 12 of the 54 engine crankshaft bearings produced during the
last shift in the plant to see how many of them had a surface finish that was rougher
than the engineering specifications required.
(a) Set up a spreadsheet of frame numbers for these bearings with the heading:
FRAME NUMBERS
(b) Then, create a separate column to the right of these frame numbers which
duplicates these frame numbers with the title: Duplicate frame numbers.
(c) Then, create a separate column to the right of these duplicate frame numbers
called RAND NO. and use the ¼RAND() function to assign random numbers to
all of the frame numbers in the duplicate frame numbers column, and change
this column format so that 3 decimal places appear for each random number.
(d) Sort the duplicate frame numbers and random numbers into a random order.
(e) Print the result so that the spreadsheet fits onto one page.
(f) Circle on your printout the I.D. number of the first 12 engine crankshaft bearings
that you would use in your test.
(g) Save the file as: RAND62
Important note: Note that everyone who does this problem will generatea different random order of bearings ID numbers sinceExcel assign a different random number each time theRAND() command is used. For this reason, the answer tothis problem given in this Excel Guide will have a completelydifferent sequence of random numbers from the randomsequence that you generate. This is normal and what is to beexpected.
220 Appendix B Practice Test
Chapter 3: Practice Test
Suppose that a manufacturer of a certain type of house paint has a factory that
produced an average of 60 tons per day over the past month for this paint. Suppose,
further, that this factory tries out a new manufacturing process for this type of paint
for 30 days. You have been asked to “run the data” to see if any change has occurred
in the production output with this new procedure, and you have decided to test your
Excel skills on a random sample of hypothetical data given in Fig. B.2
(a) Create an Excel table for these data, and use Excel to the right of the table to
find the sample size, mean, standard deviation, and standard error of the mean
for these data. Label your answers, and round off the mean, standard deviation,
and standard error of the mean to two decimal places in number format.
(b) By hand, write the null hypothesis and the research hypothesis on your printout.
(c) Use Excel’s TINV function to find the 95% confidence interval about the mean
for these data. Label your answers. Use two decimal places for the confidence
interval figures in number format.
(d) On your printout, draw a diagram of this 95% confidence interval by hand,
including the reference value.
Fig. B.2 Worksheet Data
for Chapter 3 Practice Test
(Practical Example)
Appendix B Practice Test 221
(e) On your spreadsheet, enter the result.(f) On your spreadsheet, enter the conclusion in plain English.(g) Print the data and the results so that your spreadsheet fits onto one page.
(h) Save the file as: PAINT15
Chapter 4: Practice Test
Suppose that you work for a company that manufactures small submersible pumps.
Submersible pumps are pumps that can be submerged under water and they are used
to pump water out of an area. For example, submersible pumps can be used to pump
flood water out of basements. Suppose, further, that your company has developed a
new style of pump and has decided to test it on some recently flooded homes near
Grafton, Illinois, in the USA. The old style pumps pumped an average of 46 gallons
per minute (gal/min). You want to test your Excel skills on a small sample of data
using the hypothetical data given in Fig. B.3.
Fig. B.3 Worksheet Data
for Chapter 4 Practice Test
(Practical Example)
222 Appendix B Practice Test
(a) Write the null hypothesis and the research hypothesis on your spreadsheet.
(b) Create a spreadsheet for these data, and then use Excel to find the sample size,
mean, standard deviation, and standard error of the mean to the right of the data
set. Use number format (2 decimal places) for the mean, standard deviation, and
standard error of the mean.
(c) Type the critical t from the t-table in Appendix E onto your spreadsheet, and
label it.
(d) Use Excel to compute the t-test value for these data (use 2 decimal places) and
label it on your spreadsheet.
(e) Type the result on your spreadsheet, and then type the conclusion in plainEnglish on your spreadsheet.
(f) Save the file as: PUMP8
Chapter 5: Practice Test
Suppose that an automobile repair parts manufacturer/supplier wants to test the
crash resistance of two brands of front-bumpers for 2-door passenger sedans
(BRAND X and BRAND Y). The engineer in charge of this project has decided
to test these bumpers on 2013 Honda Civics that are purposely crashed into a
cement wall at a speed of 15 miles per hour (mph), and then to estimate the cost of
repairs to the front bumper after this test. The engineer then wants to test her Excel
skills on the hypothetical data given in Fig. B.4.
Appendix B Practice Test 223
(a) Write the null hypothesis and the research hypothesis.
(b) Create an Excel table that summarizes these data.
(c) Use Excel to find the standard error of the difference of the means.
(d) Use Excel to perform a two-group t-test. What is the value of t that you obtain
(use two decimal places)?
(e) On your spreadsheet, type the critical value of t using the t-table in Appendix E.(f) Type the result of the test on your spreadsheet.
(g) Type your conclusion in plain English on your spreadsheet.
(h) Save the file as: BUMPER3
(i) Print the final spreadsheet so that it fits onto one page.
Chapter 6: Practice Test
What is the relationship between the weight of the car (measured in thousands of
pounds) and its city miles per gallon (mpg) in 4-door passenger sedans? Suppose
that you wanted to study this question using different models of cars. Analyze the
hypothetical data that are given in Fig. B.5.
Fig. B.4 Worksheet Data for Chapter 5 Practice Test (Practical Example)
224 Appendix B Practice Test
Create an Excel spreadsheet, and enter the data.
(a) create an XY scatterplot of these two sets of data such that:
▪ top title: RELATIONSHIP BETWEEN WEIGHT AND CITY mpg IN
4-DOOR SEDANS
▪ x-axis title: WEIGHT (1000 lbs)
▪ y-axis title: CITY MILES PER GALLON (mpg)
▪ move the chart below the table
▪ re-size the chart so that it is 7 columns wide and 25 rows long
▪ delete the legend
▪ delete the gridlines
(b) Create the least-squares regression line for these data on the scatterplot.
(c) Use Excel to run the regression statistics to find the equation for the least-squares regression line for these data and display the results below the chart on
your spreadsheet. Add the regression equation to the chart. Use number format
(3 decimal places) for the correlation and for the coefficients
Print just the input data and the chart so that this information fits onto one page
in portrait format.
Then, print just the regression output table on a separate page so that it fits onto
that separate page in portrait format.
By hand:
(d) Circle and label the value of the y-intercept and the slope of the regression line
on your printout.
(e) Write the regression equation by hand on your printout for these data (use threedecimal places for the y-intercept and the slope).
Fig. B.5 Worksheet Data for Chapter 6 Practice Test (Practical Example)
Appendix B Practice Test 225
(f) Circle and label the correlation between the two sets of scores in the regressionanalysis summary output table on your printout.
(g) Underneath the regression equation you wrote by hand on your printout, use the
regression equation to predict the average city mpg of a 4-door sedan that
weighted 2,500 pounds.
(h) Read from the graph, the average city mpg you would predict for a 4-door sedan
that weighed 3,600 pounds, and write your answer in the space immediately
below:________________________
(i) save the file as: sedan3
Chapter 7: Practice Test
Suppose that you wanted to estimate the total number of gallons required for 2013
4-door sedans when they were driven on a specific route of 200 miles between
St. Louis, Missouri, and Indianapolis, Indiana, at specified speeds using drivers that
were about the same weight. You have decided to use two predictors: (1) weight of
the car (measured in thousands of pounds), and (2) the car’s engine horsepower. To
check your skills in Excel, you have created the hypothetical data given in Fig. B.6.
(a) create an Excel spreadsheet using TOTAL GALLONS USED as the criterion
(Y), and the other variables as the two predictors of this criterion (X1 ¼WEIGHT (1000 lbs), and X2 ¼ HORSEPOWER).
(b) Use Excel’s multiple regression function to find the relationship between these
three variables and place the SUMMARY OUTPUT below the table.
Fig. B.6 Worksheet Data for Chapter 7 Practice Test (Practical Example)
226 Appendix B Practice Test
(c) Use number format (2 decimal places) for the multiple correlation on the
Summary Output, and use two decimal places for the coefficients in the
SUMMARY OUTPUT.
(d) Save the file as: GALLONS9
(e) Print the table and regression results below the table so that they fit onto
one page.
Answer the following questions using your Excel printout:
1. What is the multiple correlation Rxy ?
2. What is the y-intercept a ?
3. What is the coefficient for WEIGHT b1 ?4. What is the coefficient for HORSEPOWER b2 ?5. What is the multiple regression equation?
6. Predict the TOTAL GALLONS USED you would expect for a WEIGHT of
3,800 pounds and a car that had 126 HORSEPOWER.
(f) Now, go back to your Excel file and create a correlation matrix for these three
variables, and place it underneath the SUMMARY OUTPUT.
(g) Re-save this file as: GALLONS9
(h) Now, print out just this correlation matrix on a separate sheet of paper.
Answer to the following questions using your Excel printout. (Be sure to include
the plus or minus sign for each correlation):
7. What is the correlation between WEIGHT and TOTAL GALLONS USED?
8. What is the correlation between HORSEPOWER and TOTAL GALLONS
USED?
9. What is the correlation between WEIGHT and HORSEPOWER?
10. Discuss which of the two predictors is the better predictor of total
gallons used.
11. Explain in words how much better the two predictor variables combined
predict total gallons used than the better single predictor by itself.
Chapter 8: Practice Test
Let’s consider an experiment in which you want to compare the strength of beams
made of three types of materials: (1) steel, (2) Alloy A, and (3) Alloy B. The
strength of the material was measured by placing each beam in a horizontal position
with a support on each end, and then applying a force of 2,500 pounds to the center
of each beam. The “deflection of the beam” was then measured in 1/1000th of an
inch. You decide to test your Excel skills on a small sample of beams, and you have
created the hypothetical data given in Fig. B.7.
Appendix B Practice Test 227
(a) Enter these data on an Excel spreadsheet.
Let STEEL ¼ Group 1, ALLOY A ¼ Group 2, and ALLOY B ¼ Group 3.
(b) On your spreadsheet, write the null hypothesis and the research hypothesis for
these data
(c) Perform a one-way ANOVA test on these data, and show the resulting ANOVA
table underneath the input data for the three types of beams.
(d) If the F-value in the ANOVA table is significant, create an Excel formula to
compute the ANOVA t-test comparing the STEEL beams versus the ALLOY A
beams, and show the results below the ANOVA table on the spreadsheet (put
the standard error and the ANOVA t-test value on separate lines of your
spreadsheet, and use two decimal places for each value)
(e) Print out the resulting spreadsheet so that all of the information fits onto one
page
(f) On your printout, label by hand the MS (between groups) and the MS (within
groups)
(g) Circle and label the value for F on your printout for the ANOVA of the input
data
Fig. B.7 Worksheet Data for Chapter 8 Practice Test (Practical Example)
228 Appendix B Practice Test
(h) Label by hand on the printout the mean for steel beams and the mean for Alloy
A beams that were produced by your ANOVA formulas
(i) Save the spreadsheet as: STRENGTH3
On a separate sheet of paper, now do the following by hand:
(j) find the critical value of F in the ANOVA Single Factor results table
(k) write a summary of the result of the ANOVA test for the input data
(l) write a summary of the conclusion of the ANOVA test in plain English for the
input data
(m) write the null hypothesis and the research hypothesis comparing steel beams
versus Alloy A beams.
(n) compute the degrees of freedom for the ANOVA t-test by hand for three types
of beams.
(o) use your calculator and Excel to compute the standard error (s.e.) of the
ANOVA t-test
(p) Use your calculator and Excel to compute the ANOVA t-test value
(q) write the critical value of t for the ANOVA t-test using the table in Appendix E.
(r) write a summary of the result of the ANOVA t-test
(s) write a summary of the conclusion of the ANOVA t-test in plain English
Appendix B Practice Test 229
Appendix C
Answers to Practice Test
Practice Test Answer: Chapter 1 (see. Fig. C.1)
Fig. C.1 Practice Test Answer to Chapter 1 Problem